For a two-body system in absence of external forces, the kinetic energy as measured from ground frame is ${\mathrm{K}}_0$ and from centre of mass frame is ${\mathrm{K}}_{\mathrm{cm}}$ Pick up the correct statements.

Two blocks of masses $m$ and $M$ are interconnected by an ideal spring of stiffness constant $k$. If $m$ is pushed with a velocity $v_0$, then:

A block of mass $\mathrm{m}$ is placed gently onto a long plank of mass $\mathrm{m}$ moving with a velcoity $v_0$ on a smooth horizontal floor. If friction is present between $M$ and $\mathrm{m}$ :

Consider a hollow sphere of mass $M$ and radius $R$ resting on a smooth surface. A smaller sphere of mass $\mathrm{m}$ and radius $r$ is initially held at position $P$ within the bigger sphere. If the small sphere is now released, it rolls down the inner surface of hollow sphere and finally stops at its bottom point $Q.$ Then:

A long plank$\text{'}A\text{'}$ is at rest on a smooth horizontal surface. A small block ' $B$ ', whose mass is half of ' $A$ ', is placed on the plank at one end and projected along $A$ with some velocity $u.$ The coefficient of friction between the plank and block is $\mu$ :

A uniform wire frame $ABC$ is in the shape of an equilateral triangle in $xy$ -plane with centroid at the origin.

A molecule capable of vibrations is modeled as two point atoms of mass $M$ connected by a spring. Initially molecule is not vibrating when it collides elastically with a single atom of mass $M$ as shown in figure. Mark the CORRECT option(s).

Two blocks of mass ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ are connected by a spring in its natural length having spring constant $k$ and are placed on a smooth surface. Block ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ are given velocities $v$ and $v_2$ as shown in figure. Choose CORRECT statements.